Маятник Петра

Трехзвенный

g = 9.81;
m1 = 1; m2 = 1; m3 = 1;
l1 = 1; l2 = 1; l3 = 1;
timeMax = 30;

eqns = {
  (m1 + m2 + m3) l1^2 \[Theta]1''[t] + (m2 + m3) l1 l2 \[Theta]2''[t] Cos[\[Theta]1[t] - \[Theta]2[t]] +
  m3 l1 l3 \[Theta]3''[t] Cos[\[Theta]1[t] - \[Theta]3[t]] +
  (m2 + m3) l1 l2 \[Theta]2'[t]^2 Sin[\[Theta]1[t] - \[Theta]2[t]] +
  m3 l1 l3 \[Theta]3'[t]^2 Sin[\[Theta]1[t] - \[Theta]3[t]] +
  g (m1 + m2 + m3) l1 Sin[\[Theta]1[t]] == 0,
  
  (m2 + m3) l2^2 \[Theta]2''[t] + (m2 + m3) l1 l2 \[Theta]1''[t] Cos[\[Theta]1[t] - \[Theta]2[t]] +
  m3 l2 l3 \[Theta]3''[t] Cos[\[Theta]2[t] - \[Theta]3[t]] -
  (m2 + m3) l1 l2 \[Theta]1'[t]^2 Sin[\[Theta]1[t] - \[Theta]2[t]] +
  m3 l2 l3 \[Theta]3'[t]^2 Sin[\[Theta]2[t] - \[Theta]3[t]] +
  g (m2 + m3) l2 Sin[\[Theta]2[t]] == 0,

  m3 l3^2 \[Theta]3''[t] + m3 l1 l3 \[Theta]1''[t] Cos[\[Theta]1[t] - \[Theta]3[t]] +
  m3 l2 l3 \[Theta]2''[t] Cos[\[Theta]2[t] - \[Theta]3[t]] -
  m3 l1 l3 \[Theta]1'[t]^2 Sin[\[Theta]1[t] - \[Theta]3[t]] -
  m3 l2 l3 \[Theta]2'[t]^2 Sin[\[Theta]2[t] - \[Theta]3[t]] +
  g m3 l3 Sin[\[Theta]3[t]] == 0
};

initCond = {
  \[Theta]1[0] == \[Pi]/2 - 0.1,
  \[Theta]2[0] == \[Pi],
  \[Theta]3[0] == \[Pi],
  \[Theta]1'[0] == 0,
  \[Theta]2'[0] == 0,
  \[Theta]3'[0] == 0
};

sol = NDSolve[{eqns, initCond}, {\[Theta]1, \[Theta]2, \[Theta]3}, {t, 0, timeMax}];

x1[t_] := l1 Sin[\[Theta]1[t] /. First[sol]];
y1[t_] := -l1 Cos[\[Theta]1[t] /. First[sol]];
x2[t_] := x1[t] + l2 Sin[\[Theta]2[t] /. First[sol]];
y2[t_] := y1[t] - l2 Cos[\[Theta]2[t] /. First[sol]];
x3[t_] := x2[t] + l3 Sin[\[Theta]3[t] /. First[sol]];
y3[t_] := y2[t] - l3 Cos[\[Theta]3[t] /. First[sol]];

trajectories = Table[{{x1[t], y1[t]}, {x2[t], y2[t]}, {x3[t], y3[t]}}, {t, 0, timeMax, 0.05}];
trajectories = trajectories // Transpose;

Анимируем

Module[{points, tracks}, Animate[
  Graphics[
    {
      Thick, Black, 
      Line[{{0, 0}, points[[1]], points[[2]], points[[3]]} // Offload],
      Blue, PointSize[0.03], Point[points[[1]] // Offload],
      Red, PointSize[0.03], Point[points[[2]] // Offload],
      Green, PointSize[0.04], Point[points[[3]] // Offload],

      Directive[TransitionType->None],
      
      {Green, Opacity[0.15], Line[tracks[[3]] // Offload ]},
      {Red, Opacity[0.15], Line[tracks[[2]] // Offload ]},
      {Blue, Opacity[0.15], Line[tracks[[1]] // Offload ]} 
    },
    PlotRange -> {{-3.5, 3.5}, {-3.5, 0.5}},
    Axes -> True,  Frame->True,
    Background -> White, 
    ImageSize -> 450
  ], 
  {t, 0, timeMax, 0.05}, 
  AnimationRate -> 30,
  "UpdateFunction" -> Function[t,

    tracks = trajectories[[All, ;; Floor[t / 0.05] + 1]];
    points = {{x1[t], y1[t]}, {x2[t], y2[t]}, {x3[t], y3[t]}};
    
    False
  ]
] ]